The 35-year-old McCabe has long been rumored to be a target of the Rangers, and he waived his no-trade clause for the deal to be completed.
McCabe is joining his sixth NHL team. He's in the final season of a five-year, $28.75 million contract, and can become an unrestricted free agent on July 1.
He gives New York the offensive defenseman it has been seeking for the playoff push. McCabe has five goals and 17 assists in 48 games this season, and in 1,116 career NHL games with the New York Islanders, Vancouver, Chicago, Toronto, and Florida, he's posted 143 goals and 379 assists.
"Bryan McCabe adds an established veteran presence to our young defensive corps," Rangers general manager Glen Sather said in a statement. "He can help provide offense with his strong shot on the power play, and his versatility allows him to play either the left or right side effectively.
"Bryan also brings outstanding leadership qualities, having served as team captain for Florida for the past two seasons."
To make room on the roster, the Rangers assigned defenseman Michael Del Zotto to Connecticut of the AHL.
McCabe has also played in 51 playoff games, all with Toronto from 2001-04, and had 10 goals and 16 assists.
Kennedy has been stuck in the AHL all season after coming over from the Buffalo Sabres as a free agent last August. The 24-year-old left wing had 12 goals and 30 assists in 53 games at Connecticut.